We have 2 inescapable diamond losers, so we cannot afford to also lose 2 trump tricks by force or one by force and a second via a diamond ruff.
So it seems clear to start trump from the top.
Let's say that both follow small. We can guard against 4-1 on our left (if 4-1 on our right, we are, for all practical purposes, down) by leading low to our 10.
1) RHO wins... maybe they get a diamond ruff with the 3rd trump.
2) RHO shows out: now we are positioned to pick up the trump, but that will leave us a trick short even if there is no
♦ ruff available: we can't trump a spade in dummy without setting up LHO's trump length. So we are down to playing for 3 club tricks. The good news is that LHO can't lead a spade.
3) LHO wins.. and they get a diamond ruff.
The alternative is to cash the second top trump... going down on all 4-1 breaks.
It is worth bearing in mind that ducking the second trump will not always lead to a diamond ruff when one is available, since, when both follow, they will usually have had no chance to signal, even if playing suit preference in trump... assuming trump are 3-2. Estimating the percentage of time they will find the diamond ruff is very difficult.. it depends, in part, on the skill level of the opps. For example, many LHOs will be reluctant to lead from Kx if they win the 2nd trump, from QJx.
Against strong opps, I think it is clear to play the AK. Against weaker opps, it is not so clear, but I still think it is the better line.
If RHO plays an honour under the first top trump, we still have a loser if the suit is 4-1, as Ken pointed out. We should play the second top trump, because RHO could well hold QJ or QJx... it is cost free to play the Q from QJx, especially if he has a doubleton diamond.
If it turns out that trump are 4-1, then we have to drive out the remaining honour and hope that LHO is unable to negotiate a ruff. We use our 9 to accomplish this, because we want to reserve the threat of a spade ruff as our tenth trick.
Assuming that LHO negates this by clearing trump. However, when we tackle diamonds, RHO may win the first defensive trick and lead a spade. We have to hook this, since we have no trump left in dummy. If he fails to win the 1st defensive diamond trick, we are going to fall back on the club finesse, even if RHO wins the second defensive diamond trick and offers us the spade hook.
This is because we will have a good inferential count on the club suit.
If the opps play 4th best, we can assume that LHO is 4=4=3=2 (no diamond ruff, hence 3-3 or bad defence or AK tight.. 3-3 is more probable against good defenders) and this means that the odds favour the club hook.
If the opps play 3rd and low or 3rd and 5th, then LHO may well be 5=4=3=1... and didn't lead a stiff because had 4 trump. Now the (second round) club hook is 100%. If LHO is 3=4=3=3, then the club hook is even money, and the spade hook is better.
What if LHO plays an honour under the 1st top trump? If we cash the second high honour (which we should do, since trump may be 3=2), and they are 4-1 and drive out the remaining top honour, rho can lead a spade. We play the J, if it is covered, we ruff with dummy's last trump and we are in serious trouble. We can pull trump, but we have 2 diamonds to drive out, and they just pump spades at us each time. Oh well.
What if we abandon trump when LHO shows out? Play on diamonds now... we need the suit to be 3-3 anyway. Now RHO can still hurt us by playing a spade through: we hook, ruffing out RHO's Queen. Whoever wins the next diamond plays a spade, we win, and now we play a trump. If RHO wins, he can tap us with a spade, establishing his long trump. So if trump are 1=4, we need the spade Q onside and well as no diamond ruff. I won't go into the permutations if RHO leads a club through
A lot to think about... on a hand that, most of the time, is actually straight-forward to the point that probably the majority of club-level players would not even realize there was a problem
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari